不同亚型数学学习困难儿童应用题问题表征过程的研究

采用自编数学应用题解决能力测验题对小学四年级单纯型数困儿童、混合型数困儿童和普通儿童问题理解阶段、问题整合阶段的差异,以及问题表征能力与数学问题解决之间的关系进行探究。结果表明：（1）单纯型与混合型数困儿童有效识别信息的能力弱,难于利用相关信息和排除干扰信息。（2）单纯型数困儿童比混合型数困儿童更擅于运用图式表征策略。（3）图式表征策略能促进数困儿童应用题的解决。     

Distributing mathematical practice of third and seventh graders: Applicability of the spacing effect in the classroom

We examined the effect of distributed practice on the mathematical performance of third and seventh graders (N = 213) in school. Students first received an introduction to a mathematical topic, derived from their curriculum. Thereafter, they practiced in one of two conditions. In the massed condition, they worked on three practice sets in 1 day. In the distributed condition, they worked on one practice set per day for 3 consecutive days. Bayesian analyses of the performance in two follow‐up tests 1 and 6 weeks after the last practice set revealed a positive effect of distributed practice as compared with massed practice in Grade 7. In Grade 3, a positive effect of distributed practice was supported by the data only in the test 1 week after the last practice set. The results suggest that distributed practice is a powerful learning tool for both elementary and secondary school students in the classroom.     

数学焦虑对儿童加减法认知策略选择和执行的影响

根据数学焦虑量表测查结果,随机选取90名小学1~3年级的儿童为被试,每个年级30人(高、低数学焦虑者各15人).采用实验法、观察法和口语报告法相结合的方式,探讨不同数学焦虑水平儿童加减法认知策略选择和执行情况.结果发现:(1)从策略选择上看,高数学焦虑儿童使用出声策略和手势策略较多;使用对位策略较少.(2)从策略执行上看,高数学焦虑儿童出声策略、手势策略和拆十策略执行的正确率较高;竖式策略和对位策略执行的正确率较低;(3)随着儿童年级的增长,数学焦虑对其策略选择的影响越来越显著.     

数学学习障碍儿童问题解决的表征研究

本研究以小学四年级学生为被试,采用口语报告法探讨论了数学学习障碍儿童问题解决的表征情况。研究发现：数学学习障碍儿童问题解决的表征时间较短;数学学习障碍儿童问题解决的表征类型单一;数学学习障碍儿童问题解决的表征缺乏有效性。     

The long-term effects of ability grouping in mathematics: A national investigation

The complexities of school tracking have resulted in patchy explanations of how it might affect students’ academic success. We aim to develop a comprehensive understanding of tracking by investigating its long-term relationships with student outcomes. Our study is informed by sociological and social psychological theoretical perspectives that explain how this school practice may wield its influence. We use panel data from the National Education Longitudinal Survey (NELS:88) for a comprehensive analysis of the associations between ability grouping in the eighth grade and subsequent social psychological and academic variables in the 10th and 12th grades, respectively. By covering three waves of data that monitor the mathematics progress of middle school youngsters as they go through high school, we present the durable relationships of tracking. Our method compares students in tracked and untracked schools, and further partitions these students into high and low ability groups. Our results reaffirm that tracking has persistent instructional benefits for all students. Yet, high-achieving students who are tracked in middle school may suffer considerable losses in self-concept that subsequently depress their achievement, and mathematics course-taking. Implications are for a broad range theory of tracking and for further empirical work on the viability of heterogeneously-grouped classes.An earlier version of this paper was presented at the International Sociological Association (ISA) XV World Congress of Sociology, Brisbane, Australia, July 7th through 13th, 2002     

An example of formalizing recent mathematical results in Mizar

This paper describes an example of the successful formalization of quite advanced and new mathematics using the Mizar system. It shows that although much effort is required to formalize nontrivial facts in a formal computer deduction system, still it is possible to obtain the level of full logical correctness of all inference steps. We also discuss some problems encountered during the formalization, and try to point out some of the features of the Mizar system responsible for that. The formalization described in this paper allows also for contrasting the linguistic capability of the Mizar language and some of the phrases commonly used in “informal” mathematical papers that the Mizar system lacks, and consequently presents the methods of how to cope with it during the formalization. Yet, apart from the problems, this paper shows some definite benefits from using a formal computer system in the work of a mathematician.     

TPS: A hybrid automatic-interactive system for developing proofs

The theorem proving system Tps provides support for constructing proofs using a mix of automation and user interaction, and for manipulating and inspecting proofs. Its library facilities allow the user to store and organize work. Mathematical theorems can be expressed very naturally in Tps using higher-order logic. A number of proof representations are available in Tps, so proofs can be inspected from various perspectives.     

An Examination of Implicitly Activated,Explicitly Activated,and Nullified Stereotypes on Mathematical Performance: It's Not Just a Woman's Issue

This study was designed to examine the different ways that stereotypes might become activated in testing situations and the effects this activation has on task performance. In Experiment 1, women undergraduates exposed to an explicitly activated stereotype (i.e., told men outperform women in mathematics) performed worse than women exposed to a nullified stereotype (i.e., told men and women perform at the same level in mathematics). The stereotype threat also was activated implicitly under normal conditions (i.e., just given the test with nothing else stated) such that performance in this condition was at the same (low) level as the explicitly activated threat. In Experiment 2, the results were replicated with White male undergraduates using the stereotype that Asians are better than Whites in mathematics. In addition, in a small field survey we found that this belief about ethnicity did occur spontaneously for White men in college calculus courses. Taken together, the results of these studies suggest that even under normal circumstances, math test situations may lead to nonoptimal performance for both stigmatized (women) and traditionally nonstigmatized (White men) group members. Implications for threat nullification techniques are discussed.     

A Q-Methodological Study of Women's Subjective Perspectives on Mathematics

The objective of this study was to explore, using Q-methodology, women's subjective reactions to and experiences with mathematics. Ninety-six undergraduate women from a private university conducted Q-sorts on items that related to their personal experiences, attitudes, and belief/awareness of gender stereotypes for math. On the basis of the Q-factor analysis, three unique perspectives toward math emerged. The perspectives were classified as Successfully Encouraged, Stereotypically Discouraged, and Mathematically Aversive. These groupings were differentiated by their variety of experiences, attitudes, and awareness of stereotypes about math. Measures of math self-schema, math anxiety, and self-reported math ability were also used to interpret the groupings. This research revealed the women's various experiences with and attitudes toward math. The findings are integrated with previous theories in order to understand women's underrepresentation in math-related fields.